Daily Practice · Higher Plus
September 1980 5-a-day
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The batch download puts all 5 tiers' September 1980 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1980
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1980A block has mass 630 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd September 1980Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 3rd September 1980y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 4th September 1980In a vector proof you find that vector PQ = a - 6b and vector RS = 3a - 18b. What does this show about PQ and RS?
- 5th September 1980A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 6th September 1980A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 7th September 1980x = 174 and y = 113, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th September 1980f(x) = 3x - 8 and g(x) = 3x + 6. Work out fg(0).
- 9th September 1980y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 10th September 1980A cuboid measures 5 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th September 1980A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th September 1980On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th September 1980A car covers 510 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th September 1980The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 15th September 1980A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 16th September 1980A cuboid measures 6 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th September 1980A bag holds 3 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th September 1980A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 19th September 1980Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 20th September 1980A quadratic sequence starts 5, 10, 19, 32. Work out the second difference, and the coefficient of n^2.
- 21st September 1980y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 22nd September 1980The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 23rd September 1980A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 24th September 1980On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th September 1980Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
- 26th September 1980Solve x^2 - 11x + 24 < 0.
- 27th September 1980y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 28th September 1980In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 29th September 1980The probability of winning a game is 4/5. A player expects 24 wins. How many games did they play?
- 30th September 1980A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?